From Greg Williams (920106 - 2)
Bill Powers (930106.1515)
A complete model always predicts some specific outcome which
can't be confused with a different outcome, should the prediction
be wrong. The model for tracking behavior doesn't just predict
that there will be handle "movements." It says that at time t,
the handle will be _here_, at time t+0.02 sec, _here_, and so on
point by point through the whole run. There is absolutely no
equivocation in the prediction. We can, in fact, measure exactly
how far off the model is for every single data point. This is
true whether the model predicts behavior very closely or is
wildly wrong. The model presents an explanation of the behavior
that we can recognize as COMPLETE. When the explanation or model
is complete, we can tell when it is wrong, and not be concerned
whether a different interpretation might make it right. If it's
wrong it's wrong, and we can fix it. If the wrongness depends on
interpretation, there's no way to tell what needs fixing.
Using the PCT model for the tracking of a particular subject, which gives a
very high correlation between model-predicted handle positions and actual
handle positions during the course of runs with disturbances other than the
disturbance used to calibrate the model, what is the correlation between
model-predicted cursor positions and actual cursor positions during the course
of such runs? If the subject shows pseudorandom fluctuations when moving the
handle, has a reaction time lag, and occasionally hiccups, burps, or sneezes,
but the model doesn't, I suppose that the latter correlation will not be very
high. Is that true? If so, the COMPLETE model is wrong, isn't it? Then, how
would you fix it to more precisely predict cursor movement on a moment-by-
moment basis?
I see no reason why a predictive S-R model could not be developed to predict
cursor movement. But, given the pseudorandom fluctuations, I think it is
asking too much for predictions of cursor position by EITHER model to be
exact. Do you think that developing an S-R model capable of predicting cursor
movement (over a population of several trial runs) as well as the PCT model
can predict cursor movement is an impossibility?
It seems to me that a large number of models (PCT and S-R, each differing from
the others in parameters and/or basic forms) can produce equally high
correlations between actual handle position and model-predicted handle
position, because the moment-to-moment differences in the predictions of the
various models get "washed out" in computing those correlations. But trying to
predict cursor position accurately (which will necessarily involve dealing
with statistics over multiple trials, because of the inescapable noise
component) will tend to separate the good models from the poor ones.
As ever,
Greg (apparently, I'm finally rid of the old doctor -- turned out he had a
thing about women's clothes, so I gave him an old blue dress and he put it on,
danced himself into a frenzy, and exploded)